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How is a complex number a group under addition.

How is a complex number a group under multiplication(without zero)

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@chisom chinwuko: Assuming, as Ross does, that you meant "the set of all complex numbers" and "the set of all complex numbers without zero", then the answer is: in the obvious way. –  Arturo Magidin Dec 5 '10 at 22:09
The title should be changed. –  Sean Tilson Dec 5 '10 at 22:58

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A complex number is not a group under addition. The set of all complex numbers is a group under addition. Just look at the definition of a group and see that you can verify the axioms. Similarly for the set of complex numbers without zero and multiplication.

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